Related papers: Bi-Coupling Method and Applications
Diffusion and flow matching policies have recently demonstrated remarkable performance in robotic applications by accurately capturing multimodal robot trajectory distributions. However, their computationally expensive inference, due to the…
A microscopic model able to describe simultaneously the dynamic viscosity and the self-diffusion coefficient of fluids is presented. This model is shown to emerge from the introduction of fractional calculus in a usual model of condensed…
For a class of McKean-Vlasov stochastic differential equations with singular interactions, which include the Coulomb/Riesz/Biot-Savart kernels as typical examples (Examples 2.1 and 2.2), we derive the well-posedness and regularity estimates…
The rapidly increasing complexity of (mainly wireless) ad-hoc networks stresses the need of reliable distributed estimation of several variables of interest. The widely used centralized approach, in which the network nodes communicate their…
We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the…
The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
We introduce a unified statistical framework for quantifying system-environment coupling by treating the interaction energy $V_\mathcal{SE}$ as a stochastic variable. Using a reference-particle decomposition, we derive exact, closed-form…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
By using entropy and entropy production, we calculate the steady flux of some phenomena. The method we use is a competition method, $S_S/\tau+\sigma={\it maximum}$, where $S_S$ is system entropy, $\sigma$ is entropy production and $\tau$ is…
In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…
Motivated by several applications, including neuronal models, we consider the McKean-Vlasov limit for mean-field systems of interacting diffusions with simultaneous jumps. We prove propagation of chaos via a coupling technique that involves…
Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
Transfer entropy measures directed information flow in time series, and it has become a fundamental quantity in applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the…